Least Common Multiple (LCM) of 111 and 80
The least common multiple (LCM) of 111 and 80 is 8880.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 111 and 80?
First, calculate the GCD of 111 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 80 = 1 remainder 31 |
| 2 | 80 ÷ 31 = 2 remainder 18 |
| 3 | 31 ÷ 18 = 1 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 19 | 2451 |
| 37 and 61 | 2257 |
| 179 and 166 | 29714 |
| 162 and 166 | 13446 |
| 46 and 178 | 4094 |